He vowed to make the UK the fastest-growing major economy by the end of a first Labour term in government.
Making the country a "clean energy superpower" and cutting health inequalities will be other key priorities if the party wins power.
The Labour leader claimed his plan would give Britain "its future back".
The speech was an attempt by Sir Keir to convince voters Labour are a viable alternative government.
It was light on policy details - these are promised later in the year.
But it was striking that the Labour leader spoke about a "decade of renewal", hinting that he was already looking to a second term in government.
Pressed about this by journalists, he said he wanted to be "humble" and not take victory for granted, but the problems he had identified could not be fixed within five years.
Labour has a lead of around 20% over the Conservatives in opinion polls, suggesting the party is on course to win the general election which is likely to be held next year.
The five missions, which Sir Keir said would form "the backbone of the Labour manifesto and the pillars of the next Labour government", include:
* Securing the "highest sustained growth" in the G7 group of rich nations, made up of the UK, US, Canada, France, Germany, Italy, and Japan, by the end of Labour's first term
* Making Britain a '"clean energy superpower", removing fossil fuels from all of Britain's electricity generation by 2030
* Improving the NHS
* Reforming the justice system
* Raising education standards
The Labour leader's next speech, expected on Monday, will cover the economy and include what is described as a "round table" with some business leaders.
He confirmed he would back the hike in corporation tax - from 19% to 25% - coming in April, adding that businesses were more concerned about a lack of stability than the tax rise.
Critics on the left of Sir Keir's own party and within the Conservatives point out how he has shifted a long way in just a few years.
He has junked a lot of left-wing policies that got him elected as Labour leader and is now embracing language it is possible to imagine Tony Blair using.
Strategically, that may be sensible to try to woo former Conservative voters, but it leaves him vulnerable to people suggesting it is unclear what he really believes and stands for.
Addressing his audience on Thursday morning, Sir Keir said his "mission-driven government" would "restore our ambition, raise our sights above the quick fixes, the pandering to the noisy crowd, the short-termism that will only ever provide the sticking plaster".
He argued that Britain was being held back by "cynicism" and "short-term obsessions".
"We lurch from crisis to crisis, always reacting, always behind the curve," he told supporters.
In a continuation of his bid to broaden the party's appeal to voters, Sir Keir said his approach to the economy would be neither "state control" nor "pure free markets".
"I'm not concerned about whether investment or expertise comes from the public or private sector - I just want to get the job done," he said.
Conservative Party chairman Greg Hands said the Labour leader would "say anything if the politics of that moment suit him".
"He lacks principles and has no new ideas - and that is how we know a Starmer Labour government would just revert to the same old Labour habits of spending too much, raising taxes, increasing debt and soft sentences."
The left-wing campaign group Momentum attacked Sir Keir for abandoning promises he made when running for Labour leader in 2020. including introducing common ownership of energy, water and rail.
"These policies are more vital and popular now than ever - yet today, his promises lie in tatters, ditched in favour of the reheated Third-Way Blairism typified by these latest, vapid 'missions'," a spokesman said.
Sir Keir argued that "the vast majority" of Labour members supported him.
In a new year speech last month, Rishi Sunak set out his own five goals for his premiership, which, like those set out by Sir Keir, included growing the economy.
He also promised to halve inflation this year, ensure the UK's debt is falling, cut NHS waiting lists, and pass new laws to stop small boat crossings.
Some economists think inflation might already have peaked and the Bank of England has predicted it will fall midway through this year, so the prime minister is likely to meet his inflation target.
However, pledges on the NHS and small boat crossings may prove harder to achieve.